FIG. 1 is a diagram showing the configuration of a conventional filter circuit. The conventional filter circuit comprises two filters, which have respectively desired attenuation characteristic, and which are disposed in front of and behind an amplifier, respectively, to realize a steep frequency response and a high voltage gain between an input and an output of the filter circuit. More specifically, the conventional filter circuit, as shown in FIG. 1, comprises a 5th-order Low Pass Filter (abbreviated to LPF) and a 4th-order LPF disposed in the preceding and succeeding stages of the amplifier, respectively. In an article (Non-Patent Document 1), there is disclosed a receiver in which two LPFs are disposed in front of and behind an amplifier. These two LPFs, which are termed channel selection filters, for which an attenuation characteristic of 80 dB is required at the bandwidth between neighboring channels. Since a maximum voltage gain of approximately 80 dB is demanded in the baseband unit in such a direct conversion receiver, amplifiers are provided both in front of the preceding stage 5th-order LPF and behind the succeeding stage 4th-order LPF.
These three amplifiers are variable gain amplifiers (abbreviated to ‘VGA’). A high gain amplifier having a gain of 80 dB not only an input noise, but also a noise generated in the amplifier, resulting in high noise level at the output and poor signal-to-noise ratio (S/N ratio). This is why LPFs are provided separately at different stages.
Each of LPFs described in the article (Non-Patent Document 1) is an active filter and generates a noise inside the circuit, and hence the placement of noise sources and filters becomes important in order to achieve a desired S/N ratio.
In case where the amplifier in FIG. 1 is assumed to be a linear type one, the relationship between the input signal and the output signal is expressed by the product of the transfer function of the 5th-order LPF in the preceding stage of the amplifier, the voltage gain of the amplifier, and the transfer function of the 4th-order LPF in the succeeding stage of the amplifier.
Accordingly, in the frequency response of the entire circuit shown in FIG. 1, the −3 dB cut-off frequency (fc) of the entire circuit is lower than the −3 dB cut-off frequency (fc+f1) (where f1>0) of the 5th-order LPF in the preceding stage of the amplifier and the −3 dB cut-off frequency (fc+f2) (where f2>0) of the 4th-order LPF in the succeeding stage of the amplifier.
The attenuation characteristic of the 5th-order LPF in the preceding stage of the amplifier has a slope of −30 dB/Octave as from the −3 dB cut-off frequency (fc+f1) in case of the 5th-order LPF having the Butterworth characteristic. The attenuation characteristic of the 4th-order LPF in the succeeding stage of the amplifier has a slope of −24 db/Octave as from the −3 dB cut-off frequency (fc+f2) in case of the 4th-order LPF having the Butterworth characteristic.
On the other hand, since the attenuation characteristic of a 9th-order LPF has a slope of −54 dB/Octave as from the −3 dB cut-off frequency if the 9th-order LPF is a Butterworth filter, an attenuation amount of 54 dB might be obtained at a frequency which is twice the −3 dB cut-off frequency (2fc). However, only an attenuation amount of less than 50 dB is obtained at the frequency 2fc in FIG. 1.
In order to realize an attenuation amount of 50 dB or more at the frequency 2fc, it is necessary to:                increase the order of a filter by one, changing the 4th-order LPF in the succeeding stage of the amplifier to a 5th-order LPF, or        change the 5th-order LPF in the preceding stage of the amplifier to a 6th-order LPF.        
[Non-Patent Document 1]
C. Shi et al., “Design of A Low-Power CMOS Baseband Circuit for Wideband CDMA Testbed,” Proceedings of International Symposium on Low Power Electronics and Design (ISLPED 2000), 2000 Jul. 26-27, pp. 222-224, FIG. 1.